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Chapter 12

# Chapter 12 - 12 Static Equilibrium and Elasticity CHAPTER...

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12 CHAPTER OUTLINE 12.1 The Conditions for Equilibrium 12.2 More on the Center of Gravity 12.3 Examples of Rigid Objects in Static Equilibrium 12.4 Elastic Properties of Solids Static Equilibrium and Elasticity ANSWERS TO QUESTIONS Q12.1 When you bend over, your center of gravity shifts forward. Once your CG is no longer over your feet, gravity contributes to a nonzero net torque on your body and you begin to rotate. Q12.2 Yes, it can. Consider an object on a spring oscillating back and forth. In the center of the motion both the sum of the torques and the sum of the forces acting on the object are (separately) zero. Again, a meteoroid flying freely through interstellar space feels essentially no forces and keeps moving with constant velocity. Q12.3 No—one condition for equilibrium is that F = 0 . For this to be true with only a single force acting on an object, that force would have to be of zero magnitude; so really no forces act on that object. Q12.4 (a) Consider pushing up with one hand on one side of a steering wheel and pulling down equally hard with the other hand on the other side. A pair of equal-magnitude oppositely- directed forces applied at different points is called a couple. (b) An object in free fall has a non-zero net force acting on it, but a net torque of zero about its center of mass. Q12.5 No. If the torques are all in the same direction, then the net torque cannot be zero. Q12.6 (a) Yes, provided that its angular momentum is constant. (b) Yes, provided that its linear momentum is constant. Q12.7 A V-shaped boomerang, a barstool, an empty coffee cup, a satellite dish, and a curving plastic slide at the edge of a swimming pool each have a center of mass that is not within the bulk of the object. Q12.8 Suspend the plywood from the nail, and hang the plumb bob from the nail. Trace on the plywood along the string of the plumb bob. Now suspend the plywood with the nail through a different point on the plywood, not along the first line you drew. Again hang the plumb bob from the nail and trace along the string. The center of gravity is located halfway through the thickness of the plywood under the intersection of the two lines you drew. 349

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350 Static Equilibrium and Elasticity Q12.9 The center of gravity must be directly over the point where the chair leg contacts the floor. That way, no torque is applied to the chair by gravity. The equilibrium is unstable. Q12.10 She can be correct. If the dog stands on a relatively thick scale, the dog’s legs on the ground might support more of its weight than its legs on the scale. She can check for and if necessary correct for this error by having the dog stand like a bridge with two legs on the scale and two on a book of equal thickness—a physics textbook is a good choice. Q12.11 If their base areas are equal, the tall crate will topple first. Its center of gravity is higher off the incline than that of the shorter crate. The taller crate can be rotated only through a smaller angle before its center of gravity is no longer over its base.
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